# Quelques problèmes mathématiques relatifs à la modélisation des conditions aux limites fluide-solide pour des écoulements de faible épaisseur

Abstract : The problem considered in this PhD work is the asymptotic study of thin thickness flows and the modeling of the boundary conditions to impose on the fluid-solid interface in various situations. The first chapter is dedicated to the asymptotic study of a coupling between a thin film of fluid and an adjacent thin porous medium. This situation appears in boundary lubrication problems. We show that there is a critical value between the size of the microstructure of the porous medium, the free fluid gap and the thickness of the porous medium. Moreover it is shown that an actual geometry can always be described by that critical case for which a modified Reynolds equation is proved. Numerical calculations show the difference between our model and two other models proposed in the mechanical literature. In chapter 2, one is interested in the study of a thin flow behavior when one of the surface is rough. This study can be related to the preceeding chapter by considering a porous medium whith a single layer. We use the two scale convergence technique in homogenisation to obtain rigorously the convergence results. Moreover, the convergence of the normal and tangential constraints on the smooth and rough surfaces are studied. In the last chapter, we consider a micropolar fluid with new boundary conditions at the fluid-solid interface linking the velocity and the microrotation by introducing a so called boundary viscosity''. We prove the existence and uniqueness of the solution and we derive, by way of asymptotic analysis, a generalized micropolar Reynolds equation. Numerical results enhance the influence of the new boundary conditions on the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.
Keywords :
Document type :
Theses
Domain :

https://tel.archives-ouvertes.fr/tel-00005482
Submitted on : Monday, March 29, 2004 - 4:34:17 PM
Last modification on : Wednesday, July 8, 2020 - 12:42:05 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 2:20:31 PM

### Identifiers

• HAL Id : tel-00005482, version 1

### Citation

Nadia Benhaboucha. Quelques problèmes mathématiques relatifs à la modélisation des conditions aux limites fluide-solide pour des écoulements de faible épaisseur. Mathématiques [math]. Université Claude Bernard - Lyon I, 2003. Français. ⟨tel-00005482⟩

Record views